Plato thought that election by popular vote would lead to exactly what it has led to in the present: skilled orators (sophists) manipulating the average voter's (read: idiot's) emotions, rather than appealing to genuine reason. A popularity contest instead of a meritocracy. Plato was not an egalitarian; some people were more fit to rule than others, in his view. I recommend looking up Plato's "Noble Lie," also. In Republic, Plato's ideal was a very top-down structure.